Stochastic simulation
MATH-414
Course summary
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In this course, we will discuss various computational tools to analyze systems with uncertainty, as they arise in engineering, physics, chemistry, and economics. The focus will be on sampling methods as Monte Carlo, quasi-Monte Carlo, Markov Chain Monte Carlo.
Main topics include:
- Random variable generation
- Simulation of random processes
- Monte Carlo method; output analysis
- Variance reduction techniques (antithetic variables, control variables, importance sampling, ...)
- Quasi-Monte Carlo methods
- Markov Chain Monte Carlo methods (Metropolis-Hasting, Gibbs sampler)
- Stochastic optimization (stochastic approximation, simulated annealing)
- Rare events simulations
- Estimation of derivatives